Efficient manipulation of magnetic domain wall (DW) in nanostructures has drawn much attention because of its potential applications in spintronic devices such as in data storage devices [1]} and logic operations [2]}. Several controlling parameters, such as magnetic fields, microwaves, and spin-polarized currents, have been reported in the recent decade to drive DW in magnetic nanostructures. But these parameters suffer from certain limitations in applications. Particularly, in the case of magnetic-field driven, the DW propagation is obtained because of the energy dissipation [3]}, [4]}. However, the magnetic field is unable to drive a series of DWs synchronously [5]}, [6]}, [7]}. On the other hand, an electric current can drive a DW, or a series of DWs in the same direction with the mechanism of angular momentum transfer [8]}, [9]}, [10]}, [11]}. Besides, a high critical current density is required to obtain a useful DW speed, which causes a Joule heating problem. [7]}, [13]}, [14]}. To overcome such challenges, spin-wave-spin-current generated by thermal gradient (TG) emerges as an alternative driving force for the DW motion [15]}, [16]}. Therefore, the study of TG-driven DW motion is significant not only for spintronic device applications but also for the understanding of the interplay between spin-wave and magnetic DW [17]}, [18]}.
